Non-effectively Hyperbolic Characteristics

  • Tatsuo Nishitani
Part of the Lecture Notes in Mathematics book series (LNM, volume 2202)


In this chapter introducing the notion of local and microlocal elementary factorization of p, arising from standard techniques of energy integrals we prove that if p is of spectral type 1 on Σ then p always admits a local elementary factorization. On the other hand if p is of spectral type 2 even micolocal elementary factorization is not always possible. When p is of spectral type 2 near ρ we prove that p admits a “nice” microlocal factorization near ρ, which is also a microlocal elementary factorization at ρ, if the cube of some vector field H S annihilates p on Σ near ρ. This factorization is crucial to deriving energy estimates.


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© Springer International Publishing AG 2017

Authors and Affiliations

  • Tatsuo Nishitani
    • 1
  1. 1.Department of MathematicsOsaka UniversityToyonakaJapan

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